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A166024 Define dsf(n) = A045503(n) = n_1^{n_1}+n_2^{n_2}+n_3^{n_3} + n_m^{n_m}, where {n_1,n_2,n_3,...n_m} is the list of the decimal digits of n. Starting with a(1) = 421845123, a(n+1) = dsf(a(n)). 4
421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890, 421845123, 16780890 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
In fact there are only 8 loops among all the nonnegative integers for the "dsf" function that we defined.
Periodic with period 2.
LINKS
Ryohei Miyadera, Curious Properties of an Iterative Process, Mathsource, Wolfram Library Archive.
Shoei Takahashi, Unchone Lee, Hikaru Manabe, Aoi Murakami, Daisuke Minematsu, Kou Omori, and Ryohei Miyadera, Curious Properties of Iterative Sequences, arXiv:2308.06691 [math.GM], 2023.
FORMULA
a(n+1) = dsf(a(n)).
EXAMPLE
dsf(421845123) = 16780890 and dsf(16780890) = 421845123, so these 2 numbers make a loop for the function dsf.
MATHEMATICA
dsf[n_] := Block[{m = n, t}, t = IntegerDigits[m]; Sum[Max[1, t[[k]]]^t[[k]], {k, Length[t]}]]; NestList[dsf, 421845123, 4]
LinearRecurrence[{0, 1}, {421845123, 16780890}, 24] (* Ray Chandler, Aug 25 2015 *)
CROSSREFS
Sequence in context: A323537 A186795 A234193 * A234396 A017408 A017528
KEYWORD
nonn,base,easy
AUTHOR
Ryohei Miyadera, Satoshi Hashiba and Koichiro Nishimura, Oct 04 2009
EXTENSIONS
Comment and editing by Charles R Greathouse IV, Aug 02 2010
Second sentence of Name moved to Example by Michael De Vlieger, Aug 24 2023
STATUS
approved

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Last modified July 12 13:47 EDT 2024. Contains 374247 sequences. (Running on oeis4.)